How do you calculate the specific heat capacity of a piece of wood if 1500.0 g of the wood absorbs #6.75 * 10^4# joules of heat, and its temperature changes from 32°C to 57°C?

Question

Ellie Andrews · Accepted Answer

#1.8"J"/("g" ""^@"C")#

A substance's specific heat tells you how much heat much either be added or removed from #"1 g"# of that substance in order to cause a #1^@"C"# change in temperature.

This is the equation that shows the connection between specific heat, heat added or removed, and temperature change.

#color(blue)(q = m * c * DeltaT)" "#, where

#q# - the amount of heat added / removed #m# - the mass of the sample #c# - the specific heat of the substance #DeltaT# - the change in temperature

In your case, the #"1500.0-g"# piece of wood is said to absorb a total of #6.75 * 10^4"J"# of heat. This caused its temperature to increase from #32^@"C"# to #57^@"C"#.

The difference between the final temperature and the initial temperature of the sample will be the value for #DeltaT#.

#DeltaT = 57^@"C" - 32^@"C" = 25^@"C"#

This indicates that the wood's specific heat is equivalent to

#q = m * c * DeltaT implies c = q/(m * DeltaT)#

Enter your values to obtain

#c = (6.75 * 10^4"J")/("1500.0 g" * 25^@"C") = color(green)(1.8"J"/("g" ""^@"C"))#

The number of sig figs you have for the two sample temperatures is the answer, which is rounded to two.

Luna Chen · Answer

undefined The specific heat capacity of the wood can be calculated using the formula:

$$ q = mcΔT $$

where:
- $ q $ is the heat energy absorbed (in joules),
- $ m $ is the mass of the wood (in grams),
- $ c $ is the specific heat capacity of the wood (in J/g°C),
- $ ΔT $ is the change in temperature (in °C).

First, calculate the change in temperature:

$$ ΔT = 57°C - 32°C = 25°C $$

Now, substitute the given values into the formula:

$$ 6.75 * 10^4 J = (1500.0 g) * c * 25°C $$

$$ c = \frac{6.75 * 10^4 J}{1500.0 g * 25°C} $$

$$ c ≈ 1.80 J/g°C $$

So, the specific heat capacity of the wood is approximately 1.80 J/g°C.